Surface complexation models diffuse layer model

Various empirical and chemical models of metal adsorption were presented and discussed. Empirical model parameters are only valid for the experimental conditions under which they were determined. Surface complexation models are chemical models that provide a molecular description of metal and metalloid adsorption reactions using an equilibrium approach. Four such models, the constant capacitance model, the diffuse layer model, the triple layer model, and the CD-MUSIC model, were described. Characteristics common to all the models are equilibrium constant expressions, mass and charge balances, and surface activity coefficient electrostatic potential terms. Various conventions for defining the standard state activity coefficients for the surface species have been... 

To be useful in modeling electrolyte sorption, a theory needs to describe hydrolysis and the mineral surface, account for electrical charge there, and provide for mass balance on the sorbing sites. In addition, an internally consistent and sufficiently broad database of sorption reactions should accompany the theory. Of the approaches available, a class known as surface complexation models (e.g., Adamson, 1976 Stumm, 1992) reflect such an ideal most closely. This class includes the double layer model (also known as the diffuse layer model) and the triple layer model (e.g., Westall and Hohl, 1980 Sverjensky, 1993). 

The main, currently used, surface complexation models (SCMs) are the constant capacitance, the diffuse double layer (DDL) or two layer, the triple layer, the four layer and the CD-MUSIC models. These models differ mainly in their descriptions of the electrical double layer at the oxide/solution interface and, in particular, in the locations of the various adsorbing species. As a result, the electrostatic equations which are used to relate surface potential to surface charge, i. e. the way the free energy of adsorption is divided into its chemical and electrostatic components, are different for each model. A further difference is the method by which the weakly bound (non specifically adsorbing see below) ions are treated. The CD-MUSIC model differs from all the others in that it attempts to take into account the nature and arrangement of the surface functional groups of the adsorbent. These models, which are fully described in a number of reviews (Westall and Hohl, 1980 Westall, 1986, 1987 James and Parks, 1982 Sparks, 1986 Schindler and Stumm, 1987 Davis and Kent, 1990 Hiemstra and Van Riemsdijk, 1996 Venema et al., 1996) are summarised here. 

Figure 9.19. The diffuse double layer, (a) Diffuseness results from thermal motion in solution, (b) Schematic representation of ion binding on an oxide surface on the basis of the surface complexation model, s is the specific surface area (m kg ). Braces refer to concentrations in mol kg . (c) The electric surface potential, falls off (simplified model) with distance from the surface. The decrease with distance is exponential when l/ < 25 mV. At a distance k the potential has dropped by a factor of 1/c. This distance can be used as a measure of the extension (thickness) of l e double layer (see equation 40c). At the plane of shear (moving particle) a zeta potential can be established with the help of electrophoretic mobility measurements, (d) Variation of charge distribution (concentration of positive and negative ions) with distance from the surface (Z is the charge of the ion), (e) The net excess charge.

Current surface complexation models were developed with a focus on minor and trace ions and hence do not consider sorption in the diffuse layer. Even the triple-layer model (34), which can include electrolyte sorption as outer-sphere complexes, does not consider sorption in the diffuse layer. To... 

Surface complexation models can be extended to account explicitly for electrostatic sorption by calculating excess counterion concentrations in the diffuse layer in addition to specific sorption. Counterions in the diffuse layer (e.g., Ca ) can then be treated as distinct from those in bulk solution (e.g., Ca2+) and those that are specifically sorbed (e.g., =Sp-Caf). The total sorption is given by the sum of the concentrations of specifically sorbed and electrostatically sorbed species ... 

Figure 5.132 presents the ionic strength effect on the model uptake curves calculated for one proton released per one adsorbed Pb, using the diffuse layer model Kosmulski, for model parameters cf. Table 5.13). The model curves are significantly steeper, and the ionic strength effect is less significant than in the analogous Pb adsorption model (inner sphere, one proton released) combined with TLM (Fig. 5.126). The calculated stability constant of the surface complex is higher by three orders of magnitude for the diffuse layer model (Table 5.28) than for TLM (Table 5.27).

Also for other diffuse layer models (cf. Table 5.13) the calculated stability constant of silica-Pb surface complex is considerably higher than for their TLM counterparts obtained from the same experimental data. The difference between the highest and the lowest K in Table 5.28 by almost two orders of magnitude is more significant than the discrepancies between the stability constants calculated for different diffuse layer models obtained for alumina (cf. Table 5.22). In spite of different K, the course of the calculated uptake curves obtained for different diffuse layer models and one proton released per one adsorbed Pb with... 

In the diffuse layer model the surface reactions include Eqs. (6.6) and (6.7) for protonation and dissociation of the surface functional groups. In the two-site version of the model, surface complexation with metals is considered to occur on at most two types of sites a small set of high-affinity strong sites, S OH, and a large set of low-affinity weak sites, S OH, analogous to Eq. (6.8) (Dzombak and Morel, 1990) ... 

The intrinsic equilibrium constants for the diffuse layer model are similar to those for the constant capacitance model where P is replaced by Equations (6.10) and (6.11) describe surface protonation and dissociation, respectively. Metal surface complexation is described by two constants similar to tliat defined in Eq. (6.12) for strong and weak sites ... 

Figure 6.6. Fit of the diffuse layer model to copper adsorption by hydrous ferric oxide. The solid line represents the optimal ht for these data. The dashed line represents the fit corresponding to the best overall estimate of the Cu surface complexation constant obtained from 10 Cu adsorption edges. (From Dzombak and Morel. 1990.)...

In the diffuse layer model, all intrinsic metal surface complexation constants were optimized with the FITEQL program for both the strong and weak sites using the best estimates of the protonation constant, log X +(int) = 7.29, and the dissociation constant log K-(int) = —8.93 obtained with Eq. (6.61) (Dzombak and Morel, 1990). Thus, individual values of log A . (int) and log A . (int) and best estimates of log (int) and log A j (int) are unique in that they represent a self-consistent thermodynamic database for metal adsorption on hydrous ferric oxide. 

Another standardized database for the diffuse layer model was developed for montmorillonite by Bradbury and Baeyens (2005). Surface complexation constants for strong and weak sites and cation exchange were fit to adsorption data for various metals using constant site densities and protonation-dissociation constants in a nonelectrostatic modeling approach. Linear free energy relationships were developed to predict surface complexation constants for additional metals from their aqueous hydrolysis constants. 

Constant capacitance model (CCM) was proposed in 1972 by Schindler and Stumm (Schindler, R. W. et at, 1976 Stumm, W. et at, 1980) mostly for the surface of oxides. It is based on the very first model of the dual electric layer developed by Helmholtz. Its core concept is an assumption that only inner-sphere ion complexes form, which are positioned as an individual layer at some distance from the surface, and the diffusion layer is absent. It is believed that Na+, K+, Cb and NO ", as well as inert, do not form bond with the surface and affect only the ion force of the solution. For this reason the model is viewed as two parallel capacitor plates surface of the mineral with charge a, on the one hand, and adsorbed H+, OH and other ions (Figure 2.18, A) with charge + a. on the other. At that, the electric potential value on the surface of the mineral is equal to... 

For the use of the diffusion layer model are ne ed parameters of active centre concentration and acidity constants Kp and Kd on the mineral s surface and also equilibrium constants of all specific complexation reactions. This model was successfully used at analysis of adsorption of such ions as Na+, SO or Cl poorly adsorbed on the surface of iron oxide type minerals. 

G. H. Bolt, Soil Chemistry. B Physico-Chemical Models, 2nd rev. ed. Elsevier, Amsterdam, 1982. Chapter 2 surveys diffuse double layer theory as applied in soil chemistry, and Chap. 13 surveys surface complexation models. 

Another major disadvantage of the commonly used surface complexation models, and of most equilibrium-based sorption models, is that three-dimensional surface products are not included as possible complexes. However, there are several exceptions. Farley et al. (5) and James and Healy (6) considered surface precipitation in successfully modeling sorption of hydrolyzable metal ions. Dzombak and Morel (7) modified the diffuse layer surface complexation model to include surface precipitation. However, these applications relied solely on macroscopic data without molecular-level identification of the sorption complex structure. Recently, Katz and Hayes (8,9) employed triple layer models, that included a surface solution model, a surface polymer model, and a surface continuum model to describe molecular level data for Co sorption on y-AljOj over a wide range of surface coverages (0.1 to 100%). 

Hgure 2 (A) Calculated adsorption by a hydrous ferric oxide of several metal cations at a tolal added melal concentration of 10 mol I using the diffuse double layer surface complexation model. (From Dzombak DA and Morel FMM (1990) Surface Complexation Modeling Hydrous Ferric Oxide. New York Wiley.) (B) Experimentally measured cadmium ([Cd]total = 0.3 mmol I h adsorption by O (open circles) and B (filled circles) horizons (18.5gdm ) in 0.01 moll NaNOs. (Data from Lumsdon DG (2004) Partitioning of organic carbon, aluminium and cadmium between solid and solution in soils application of a mineral-humic particle additivity model. European Journal of Soil Science, in press.)... 

Fig. 3 Experimental points of net proton surface excess amounts from the reversible backward titration cycles of sodium montmoril-lonite at different NaCl concentrations. The different lines represent the results of numerical fitting (FITEQL [28]) using the diffuse-double-layer option of the surface complexation model assuming reactions of and Na" ions with permanently charged ion-exchange sites in parallel with protonation/deprotonation reactions on amphoteric edge sites...

In the following sections, different surface complexation models will be introduced. General aspects and specific models will be discussed. The components of surface complexation theory will be presented, as well as some recent developments covering, for example, the use of equations for the diffuse part of the electrical double layer for electrolyte concentrations, for which the traditional Gouy-Chapman equation is not recommended or a generalization of Smit s compartment model [6] for situations in which the traditional models are at a loss. 

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